1. Field of the Invention
The invention relates to improvements in methods and apparatus for reducing vibration induced noise in machinery, and in particular, to a method and apparatus for actively cancelling vibrations in a structure supporting rotating machinery.
2. Prior Art
It is desirable to reduce or eliminate vibrations induced in rotating machinery. Various active and passive methods have been employed to suppress vibrations. For example, passive methods include cushion supports and mechanical damping means which in essence absorb and dissipate the vibrational energy produced by the disturbance. Passive methods are generally unsatisfactory because the vibrational energy is ultimately transferred to the environment. This occurs because the vibrational energy contains complex wave forms which manifest themselves at various harmonics of the fundamental vibration frequency. A simple mechanical absorber or damper may thus be essentially transparent to various components of the vibrational energy. Accordingly, such efforts to suppress, cancel or eliminate the vibrations may not be effective.
Active methods are more successful at eliminating or cancelling vibrations. However, these too have deficiencies. Like passive methods, active methods may only be operable within a narrow frequency range of the fundamental disturbance. In active systems a counteractive force is produced which opposes the force produced by the disturbance. The opposing force is not easily generated with accuracy because the nature of the disturbance is unknown. The problem is further aggravated by the fact that the structure may be complex and is not amenable to a simplified rigid body analysis.
3. Related Invention
A method for reducing or cancelling vibration induced in rotating machinery is disclosed in a copending patent application Ser. No. 375,227, filed on July 3, 1989 now U.S. Pat. No. 4,950,966 which issued Aug. 21, 1990. In the application, the teachings of which are incorporated herein by reference, unwanted vibration in the mechanical structure 10 caused by a periodic pulsating force 12 in a rotating shaft 14 can be cancelled by the arrangement illustrated in FIGS. 1A-1C.
A reaction mass actuator or forcer 16, acting on the shaft 14 through a permanent magnet or electromagnet 18 applies a controlled counteractive force 20 to the shaft 14 which opposes the shaft pulsation force 12. The actuator 16 operates in response to an output of adaptive vibration canceller 22. The counteractive force 20 cancels the vibrations in the structure as measured by the velocity or acceleration sensor 24 which is physically remote from the forcer 16 as illustrated. The adaptive vibration canceller (AVC) 22 generates weighted sinusoidal force components which follow the harmonic frequencies of the shaft pulsation force 12. In the system described, rotation speed .omega. of the shaft 14 is measured by an optical or magnetic incremental encoder 26 which produces output pulses in synchronism with the rotation of the shaft 14. The output of the encoder 26 is harmonically related to the shaft pulsation force 12. Accordingly, shaft rotation speed .omega. and force output 20 are related.
In the arrangement illustrated, a rotational harmonic generator 28 (FIGS. 1A and 1B) responsive to the encoder 26 produces various time base sinusoidal signals 29 at the fundamental rotational speed .omega. of the shaft 14 and at harmonics thereof. The time base sinusoidal signals or outputs 29 of generator 28 are in the form: e.sup.jkwt, where k is an integer 1, 2, 3 . . . n and .omega. is the speed of the shaft 14. The outputs of the generator 28 are used to generate weighted force component signals 30 in adaptive vibration canceller 22 at the various selected harmonics. The actuator 16 may thus be controlled by means of adaptive vibration canceller 22, encoder 26 and the generator 28 at the fundamental shaft rotation frequency and at various selected harmonics thereof. It is to be understood that because harmonic frequencies of the force components are based upon the encoder outputs, the weighted force components 30 follow the harmonic of the pulsation force or disturbance 12 as the shaft rotation speed varies. Other vibration cancellation schemes based on FFT or time-domain methods would use the same time base, but would not generate the same sinusoidal waveforms.
Any number of harmonics may be employed to produce the desired force components. For the purpose of this discussion, only the kth harmonic is illustrated it being understood that the sum of the various selected harmonics drive the actuator 16.
In the illustration (FIG. 1C), the disturbance or pulsation force 12 may be represented as a complex number in the form of A sin kwt and B cos kwt. A and B are unknown coefficients of a single complex number. The weighted force components 30 are signals which drive forcer 16 and are also represented in the form C sin and D cos where C and D are the weighted coefficients of a complex number. The values of C and D are varied to thereby control the response of the forcer 16. Sin and cos components are supplied by the generator 28 at kth harmonic.
The entire structure 10 has a system dynamic characteristic 32 which is in the form of G&lt;.phi. where G is the gain at the kth harmonic represented by the ratio of the accelerometer output 25 over the actuator input 30, and .phi. is the phase angle between the signals.
In the arrangement FIG. 1C, the mechanical disturbance 12 is mechanically combined with the counter active force 20 of the forcer 16 by interaction with the structure 10. The resulting physical acceleration E is detected by sensor 24 (e.g., accelerometer). The output 25 of sensor 24 is coupled to adaptive vibration canceller 22 wherein it is multiplied at 36 and integrated over time at 34 in the preprocessor 40 by the kth harmonic from the generator 28. The outputs 38 are Fourier coefficients of E in the form of sin wt and cos wt and feed adaptive algorithm processor 42 which produces weighted components C and D which are combined with the generator outputs to produce weighted force component outputs 30 for driving forcer 16.
In the arrangement described for one forcer 16 and one sensor 24, the adaptive algorithm processor 42 solves two linear equations for the two unknowns A and B which then determine the weighted values C and D. The combined weighted force component signals C sin kwt, D cos kwt, 30 drive the forcer 16 at the kth harmonic.
In the current harmonic (or Fourier series) based algorithm the sine and cosine waveforms at each harmonic frequency are multiplied by adaptively adjusted weights C and D and are then summed with the corresponding sines and cosines from the other harmonics to determine the controlled force 20 applied to the shaft 14 via the reaction mass actuator or forcer 16. The accelerometer measurement signal (which must be minimized in an adaptive vibration cancellation system) is resolved into its Fourier components by separately multiplying it by the sine or cosine of each harmonic frequency and integrating the product over an entire cycle of shaft rotation, obtaining two error signal Fourier coefficients at each harmonic frequency. The Fourier coefficients at a given frequency are then used to adjust the actuator adaptive weights at that same frequency, so as to minimize these error signal Fourier coefficients themselves. As long as the mechanical vibrational system is linear, the adaptation process at one harmonic frequency will not interact with the adaptation at any other harmonic frequency. These operations for the kth harmonic summarized in FIG. 1C may thus be combined with other harmonics of interest.
The arrangement described more fully and in greater detail in the above-identified application is directed to a single forcer, single accelerometer system and does not address the problem of reducing vibrations at various locations in a complex structure. The problem is complicated by the fact that the number of actuators is usually fewer than the number of accelerometers. Also, to be most effective, actuators should be designed into the equipment and not merely added on. This greatly reduces the number of available actuator locations. Thus the cost of such equipment is considerably increased for each actuator provided.